Hi Catarina,
It is my understanding that you are trying to generate the all possible combinations for the matrix M using T row vectors.
I am assuming that for each row T can take one of following possible 4 values
1. {1,0,0}
2. {0,1,0}
3. {0,0,1}
4. {1,1,1}
So for each row, there are 4 options available to fill that row.
No. possible combinations = 4*4*4*.. (8 times) = 4^8 = 65536
To generate all possible combinations recursion can come handy, you can see the below code for reference.
% All possibilities for T
% The initial matrix with symbolic placeholders (1, 2, 3)
% representing t1, t2, t3
T_possibilities = [
1, 0, 0;
0, 1, 0;
0, 0, 1;
1, 1, 1
];
% Initialize the original matrix M with symbolic placeholders
M_template = [
1, 2, 3, 0, 0, 0;
1, 0, 2, 3, 0, 0;
1, 0, 0, 2, 3, 0;
1, 2, 0, 0, 3, 0;
0, 1, 2, 0, 0, 3;
0, 0, 1, 2, 0, 3;
0, 0, 0, 1, 2, 3;
0, 1, 0, 0, 2, 3
];
% All possibilities for T
% The initial matrix with symbolic placeholders (1, 2, 3)
% representing t1, t2, t3
T_possibilities = [
1, 0, 0;
0, 1, 0;
0, 0, 1;
1, 1, 1
];
% Initialize the original matrix M with symbolic placeholders
M_template = [
1, 2, 3, 0, 0, 0;
1, 0, 2, 3, 0, 0;
1, 0, 0, 2, 3, 0;
1, 2, 0, 0, 3, 0;
0, 1, 2, 0, 0, 3;
0, 0, 1, 2, 0, 3;
0, 0, 0, 1, 2, 3;
0, 1, 0, 0, 2, 3
];
% Function to generate all combinations recursively
function combinations = generate_combinations(M_template, T_possibilities, row, combinations)
if row > size(M_template, 1)
combinations{end+1} = M_template;
return;
end
for i = 1:size(T_possibilities, 1)
T = T_possibilities(i, :);
M_row = M_template(row, :);
for j = 1:3
% replace the placeholders (1, 2, 3) with the corresponding
% elements from T
M_row(M_row == j) = T(j);
end
new_template = M_template;
new_template(row, :) = M_row;
combinations = generate_combinations(new_template, T_possibilities, row + 1, combinations);
end
end
% Generate all possible combinations
all_combinations = generate_combinations(M_template, T_possibilities, 1, {});
% Display the number of combinations
fprintf('Total combinations: %d\n', length(all_combinations));
disp('Example combinations:');
%% Display sample combination
disp(all_combinations{1});
disp(all_combinations{2});
The above MATLAB code defines a matrix M with symbolic placeholders (1, 2, 3) and a set of possible transformation matrices T. It recursively generates all combinations of M by replacing placeholders with elements from T. Each combination results in a modified matrix M, and all such combinations are stored in 'all_combinations'.
Thanks
